What Is an Attributive Adjective?
Miles Rind and Lauren Tillinghast
Peter Geach’s distinction between logically predicative and logically attributive adjectives,
first advanced just over fifty years ago, has become part of the technical apparatus of
philosophers.1 For all that, no satisfactory explanation of what an attributive adjective is
has yet been provided. We argue that Geach’s discussion suggests two different ways of
understanding the notion. According to one, an adjective is attributive just in case
predications of it in combination with a noun fail to behave in inferences like a logical
conjunction of two separate predications. According to the other, an adjective is attributive
just in case it cannot be applied in a truth-value-yielding fashion unless combined with a
noun. We argue that the latter way of understanding the notion yields both a more
defensible version of Geach’s arguments that ‘good’ and ‘bad’ are attributive and a more
satisfactory explanation of attributivity.
1. Inferential Irregularity
Geach introduces the terms ‘logically predicative adjective’ and ‘logically attributive
adjective’ as follows:2
1. P. T. Geach, ‘Good and Evil’, Analysis 17 (1956): 33–42. All quotations in what
follows are from pp. 33–34 of this article. For recent instances of the use of ‘attributive
adjective’, see Philippa Foot, Natural Goodness (Oxford: Clarendon Press, 2001), 2–3;
Rosalind Hursthouse, On Virtue Ethics (Oxford: Oxford University Press, 1999), 195–196;
Stephen Read, Thinking about Logic: An Introduction to the Philosophy of Logic (Oxford:
Oxford University Press,1994), 176; and Judith Jarvis Thomson, ‘The Right and the Good’,
The Journal of Philosophy 6 (1997): 277.
2. Frank Sibley claims that ‘we need, but are never given’ in Geach’s article a
‘definition or elucidation’ of the terms ‘logically predicative’ and ‘logically attributive’
What Is an Attributive Adjective?
2
I shall say that in a phrase ‘an A B’ (‘A’ being an adjective and ‘B’ being a noun) ‘A’ is
a (logically) predicative adjective if the predication ‘is an A B’ splits up logically into a
pair of predications ‘is a B’ and ‘is A’; otherwise I shall say that ‘A’ is a (logically)
attributive adjective.
Before we examine this passage, a few points of terminology are in order. First, following
Geach, we shall hereafter omit the qualification ‘logically’ from the terms ‘predicative’ and
‘attributive’. Second, Geach’s use of the term ‘predication’ here is unusual. In other
writings, he uses it to signify a sentence or a phrase in which a predicate is applied to
something, and uses the word ‘predicate’ for what he here calls a ‘predication’.3 The latter
usage is more common, and it is the one that we shall follow. Finally, for the sake of
brevity, we shall call predicates of the form ‘is an A B’ ‘complex predicates’.
In the quoted passage, Geach distinguishes between complex predicates that ‘split up
logically’ into a pair of predicates and ones that do not so split up, and uses this distinction
in turn to distinguish between predicative and attributive adjectives. According to the
passage, if a complex predicate splits up logically, then the adjective in it is predicative; if
it does not, the adjective is attributive.
Since Geach offers no explanation of what it means for a complex predicate to ‘split
up logically’, we are left to determine the content of the notion for ourselves. An obvious
way to do this is to examine the considerations by which he justifies applications of the
notion. Immediately after introducing the predicative–attributive distinction, Geach
observes that predications of the phrases ‘big flea’ and ‘small elephant’ do not split up
logically—‘for’, he says, ‘if these analyses were correct, a simple argument would show
(‘Adjectives, Predicative and Attributive’, in Sibley, Approach to Aesthetics: Collected
Papers on Philosophical Aesthetics, edited by John Benson, Betty Redfern, and Jeremy
Roxbee Cox (Oxford: Clarendon Press, 2001), 156). We take the quoted passage to be
intended as just such a definition or elucidation. We also reject, for reasons that will
become apparent in what follows, Sibley’s view that the arguments that Geach provides
for holding that certain adjectives are attributive imply several different ‘tests’ of
attributivity, each yielding different results.
3. See Geach, ‘Ascriptivism’ and ‘Assertion’, both reprinted in Geach, Logic Matters
(Berkeley and Los Angeles: University of California Press, 1972).
What Is an Attributive Adjective?
3
that a big flea is a big animal and a small elephant a small animal.’ Geach’s reasoning
may be elaborated thus:
(1) The following argument is not valid:
(1.1) Whatever is a flea is an animal.
(1.2) Therefore, whatever is a big flea is big animal.4
(2) Any argument of the following form is valid:
(2.1) Whatever is an F is an A.
(2.2) Therefore, whatever is an F and is B is an A and is B.
(3) Therefore, the first argument cannot have the same logical form as the second.
(4) Therefore, ‘is a big flea’ does not split up logically into ‘is a flea’ and ‘is big’ (and
the same, mutatis mutandis, for ‘small elephant’).
The disparity in logical status between the sample argument (1.1)–(1.2) and the schematic
argument (2.1)–(2.2) shows that the two do not correspond in logical form, and thus that ‘x
is a big flea’ does not correspond in logical form to the conjunction of a pair of
predications.5
These examples suggest that a complex predicate ‘splits up logically’ just in case
applications of it enter into inferences according to the same forms as apply to a
conjunction of predications. Accordingly, a predicative adjective will be an adjective,
applications of whose complex predicates license inferences in the fashion of logical
conjunctions, and an attributive adjective will be an adjective, applications of whose
complex predicates fail to license inferences in this fashion. For convenience, we shall
4. The intended argument might also be: ‘a is a big flea; every flea is an animal;
therefore, a is a big animal’. This requires a different schematic argument in step (2), but
the overall course of reasoning is the same.
5. If one presumes at the outset that ‘x is a big flea’ can be represented by ‘Fx & Bx’,
as does John Donnelly (‘Some Remarks on Geach’s Predicative and Attributive Adjectives’,
Notre Dame Journal of Formal Logic 12 (1971): 125–128), one is most likely to find
Geach’s distinction incoherent—as, again, does Donnelly. He is criticized on the point by
John Stevenson (‘Donnelly on Geach’, Notre Dame Journal of Formal Logic 13 (1972):
429–430).
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4
describe complex predicates whose applications do not behave in the manner of logical
conjunctions as inferentially irregular.
The examples also suggest that one way to show that an adjective is attributive is to
provide a sample argument using the adjective in such a way that (i) the argument itself
is invalid, and (ii) the schema that one gets by treating all applications of complex
predicates with the adjective in the original argument as conjunctions is valid. For
convenience, we shall call the latter the predicative counterpart of the original argument.
This understanding allows us to make sense of Geach’s rather cursory account of two
more examples—‘putative’ and ‘forged’:
Again, the sort of adjective that the mediaevals called alienans is attributive; ‘x is a
forged banknote’ does not split up logically into ‘x is a banknote’ and ‘x is forged’, nor
‘x is the putative father of y’ into ‘x is the father of y’ and ‘x is putative’.
Although Geach offers no argument for this assertion, the notion of inferential irregularity
indicates where to look for one. For it is evident that from ‘x is a forged banknote’, one
cannot validly infer ‘x is a banknote’, and from ‘x is the putative father of y’, one cannot
validly infer ‘x is the father of y’. (This invalidation of the inference from ‘x is an A B’ to ‘x
is a B’ seems to be what Geach means by calling an adjective ‘alienans’.)6
One further clarification: It is obvious that, when Geach uses the letters ‘A’ and ‘B’ as
proxies for an adjective and a noun, respectively, each stands, in a given substitution, for
the same adjective or noun in all occurrences. What may not be obvious is that the
sameness is not merely in respect of spelling, pronunciation, and etymology, but also
sense. Thus, e.g., the fact that ‘x is a red herring’ (the idiom, not the description of a fish of
a certain colour), does not license the same inferences as ‘x is red and x is a herring’ does
6. One part of medieval logic was the analysis of ways in which a term may be
‘alienated’ from its customary ‘status’, ‘supposition’, or ‘appellation’. See, e.g., John
Buridan, Summulae de dialectica, translated by Gyula Klima (New Haven: Yale
University Press, 2001), 301–302.
What Is an Attributive Adjective?
5
not show ‘red’ to be attributive.7 With respect to sense, ‘red’ is no more a component of the
idiom ‘red herring’ than are the words ‘her’ and ‘ring’.
The explanation of attributivity in terms of inferential irregularity has several
virtues: it makes sense of Geach’s treatment of the examples that he gives of attributive
adjectives; it yields a natural account of his claim that alienans adjectives are attributive;
and it seems to afford a semi-rigourous way of proving that a given adjective is
attributive—‘semi-rigourous’ in that we can appeal to canonical forms of inference to show
that an argument of a given form is valid or invalid, even though the claim that a given
argument in natural language has this or that logical form is not itself amenable to
rigourous proof.
2. Difficulties with Inferential Irregularity
However, the notion of inferential irregularity is much less helpful when we turn to
Geach’s arguments that ‘good’ and ‘bad’ are attributive. Indeed, if his arguments are taken
to rely on that notion, they seem to fail entirely.
Geach’s arguments for the attributivity of ‘good’ and ‘bad’ are both presented very
briefly. Here is the pertinent passage on ‘good’:
I could ascertain that a distant object is a red car because I can see it is red and a
keener-sighted but colour-blind friend can see it is a car; there is no such possibility
of ascertaining that a thing is a good car by pooling independent information that it is
good and that it is a car. This sort of example shows that ‘good’ . . . is essentially an
attributive adjective.
If we try to understand this passage in terms of inferential irregularity, we immediately
7. Sibley (158–159) excludes seeming occurrences of adjectives within idioms and
technical terms as well as equivocal occurrences of adjectives from the scope of Geach’s
distinction, but does so in a merely ad-hoc fashion.
What Is an Attributive Adjective?
6
run into difficulties. For the only argument that it suggests is one on the following lines:8
(1) That distant object is good.
(2) That (same) distant object is a car.
(3) Therefore, that (same) distant object is a good car.
If this argument is to show the inferential irregularity of ‘good car’, then, as has been
noted, (i) it must be invalid, and (ii) its predicative counterpart must be valid. But, on the
assumption that every one of the sentences (1)–(3) is logically well-formed, one could hold
their sequence to meet the first condition only by supposing that some expression in them,
presumably ‘good’, is employed equivocally; and if that were the case then the predicative
counterpart of the argument would have to use more than one predicate letter to stand for
different occurrences of the supposedly equivocal word. It would therefore also be invalid,
and the original argument would consequently fail to meet the second condition. Thus, the
example fails to reveal inferential irregularity.
One faces even greater difficulties in finding a proof of attributivity in the passage
about ‘bad’. Geach writes:
[That ‘bad’ is attributive] is fairly clear . . . because ‘bad’ is something like an
alienans adjective; we cannot safely predicate of a bad A what we predicate of an A,
any more than we can predicate of a forged banknote or a putative father what we
predicate of a banknote or a father. We actually call forged money ‘bad’; and we
cannot infer e.g. that because food supports life bad food supports life.
For a start, it is not clear how one is to take Geach’s point about ‘bad’ being ‘something
like’ an alienans adjective. One may be tempted to construe it as implying the following
8. Alfred F. MacKay (‘Attributive–Predicative’, Analysis 30 (1970): 118–119) and
Charles Pigden (‘Geach on “Good”’, The Philosophical Quarterly 49 (1990): 131–132) both
read the quoted passage as an attempt (and an unsuccessful one) to establish the
attributivity of ‘good’ by exhibiting a failure of inference along the lines indicated.
What Is an Attributive Adjective?
7
argument: alienans adjectives are attributive; ‘bad’ is ‘something like’ an alienans
adjective; therefore, ‘bad’ is attributive. Such an argument would be a miserable non
sequitur; for without a specification of the respect in which ‘bad’ is like an alienans
adjective, and a proof that the respect in question is what makes alienans adjectives
attributive, the conclusion does not follow.9
But perhaps the likening of ‘bad’ to alienans adjectives is merely an expository device.
The nerve of the argument would then be the claim that, when ‘bad’ is applied to some
object in combination with some substantive ‘A’ (e.g., ‘food’), we cannot make those
predications of the object which we otherwise make of an A (e.g., ‘supports life’). That
would be the respect in which ‘bad’ is like an alienans adjective. So understood, the
passage at least does not fall flat on its face argumentatively; but there remains the
question how this fact about ‘bad’ is supposed to show that it is attributive. The difficulty
this time is that the statement ‘Food supports life’ must figure as a premiss and yet has no
determinate logical quantity. Should it be understood as a strictly universal statement,
‘All food supports life’, or as a merely general one, such as ‘Most food supports life’?
Neither option gets us what we are after.
To see this, suppose that we take the premiss to be a universal statement. We then
get the argument: ‘All food supports life; therefore, bad food supports life.’ Obviously, the
argument rests on a false premiss: some food presumably does not support life, namely
some bad food.10 But if it were true that all food supports life, the conclusion would follow
without a hitch. The argument is therefore valid (even though not sound) and accordingly
provides no evidence that ‘bad’ is attributive.
The other option is to take the premiss to be a rough generalization, such as ‘Most
food supports life’. We then get the argument: ‘Most food supports life; therefore, bad food
supports life.’ This is certainly an invalid argument; but it is not an argument whose
predicative counterpart is valid: from ‘Most F is G’ one cannot infer ‘Such and such F is
9. MacKay (115) interprets and criticizes the passage in just this fashion.
10. MacKay (117) imputes to Geach the view that bad food is not food. Aside from
being implausible in itself, such an idea is at odds with the thesis that ‘bad’ is ‘something
like’ an alienans adjective. If ‘x is bad food’ entailed ‘x is not food’, ‘bad’ would not be
‘something like’ an alienans adjective but would be one.
What Is an Attributive Adjective?
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G’.11 Again, the argument does not show that ‘bad’ is attributive.
Thus, so long as Geach’s examples with ‘good’ and ‘bad’ are interpreted in terms of
inferential irregularity, they manifestly fail to show that those adjectives are attributive.
3. Substantive-dependence
But suppose that, instead of assuming that inferential irregularity is the key to
understanding Geach’s arguments that ‘good’ and ‘bad’ are attributive, we ask what
conception of attributivity his arguments require. If we do so, we find that, in these cases,
what makes an adjective attributive is the fact that it cannot be used to make a logically
complete predication unless it modifies some substantive expression.12 For convenience,
we shall say that, according to this conception, an adjective is attributive just in case it is
substantive-dependent.13
Consider, again, the point about ‘good’. If Jones can see that the speck in the distance
is red, and keen-eyed but colour-blind Smith tells him that it is a car, Jones can conclude
that the thing in question is a red car: so why can there not be a corresponding case with
‘good’—one in which Jones supplies the judgment that that thing is good, Smith tells him
that it is a car, and Jones concludes that it is a good car? The obvious answer is that there
is no such thing as ‘judging that a thing is good when one does not know what the thing
11. Pigden takes Geach to be claiming that ‘we cannot infer that because food usually
sustains life, bad food will sustain life’ (131; author’s italics). Oddly, he takes this to show
that ‘bad’ is attributive—though only in the phrase ‘bad food’, not in general.
12. Sibley appears to recognize this element of Geach’s conception when he notes that
certain adjectives discussed by Geach are such that attempts to predicate them without an
attendant substantive are ‘somehow incomplete . . . hence not fully intelligible, and hence
can have no truth-value assigned to them’ (158). He claims, however, that this does not
hold true of all attributive adjectives.
13. Austin’s term ‘substantive-hungry’ (J. L. Austin, Sense and Sensibilia, edited by
G. J. Warnock (Oxford: Clarendon Press,1962), 68–70) is more colourful but less apt, as
attributive adjectives remain dependent on substantives even when their appetite for
them has been momentarily satiated. It may be noted that one of Austin’s examples of a
‘substantive-hungry’ adjective is ‘good’.
What Is an Attributive Adjective?
9
is’. To say, ‘That thing in the distance, whatever it is, is good’, is to talk vacuously. Such
an utterance is not a logically complete sentence: ‘is good’, used without a substantive,
either in explicit combination with it or, as Geach says, ‘supplied from the context’, is not a
genuine predicate at all. The example thus appears to be an attempt to show that ‘good’ is
attributive by drawing attention to its substantive-dependent character.
Geach’s argument about ‘bad’ also fares better when understood along these lines. To
see this, recall that Geach’s main claim about ‘bad’ is that ‘we cannot safely predicate of a
bad A what we predicate of an A’. Geach contrasts this point about ‘bad’ with a companion
observation about ‘good’, that ‘whatever holds true of an A as such holds true of a good A’.
The idea appears to be that, if one is to say of some A that it is a bad A (or simply that it is
bad A, if ‘A’ is a mass term), there must be some predicates that are true of an A as such,
or in kind, even though they do not hold true of every A (e.g., ‘supports life’ holds of food as
such, but not of everything that is food). To say of some A that it is a bad A is to say that
some such predicate (one or more) is not true of it. Now, provided that this holds for the
use of ‘bad’ quite generally, and not merely for its use as a qualifier of nouns, it plainly
follows that any attempt to apply ‘bad’ without applying it to qualify some particular
substantive fails to constitute a genuine predication. Thus ‘bad’ is substantive-dependent,
and therefore attributive.
For present purposes, it is not necessary to find these arguments for the attributivity
of ‘good’ and ‘bad’ conclusive. The idea of what may ‘safely’ be predicated of an A is far
from perspicuous, and it may not be taken for granted that ‘good’ and ‘bad’ have only the
sort of use that Geach describes. But this should not obscure the fact that neither
argument is the non-starter it has struck critics as being. Our point is merely that Geach’s
treatment of ‘good’ and ‘bad’ rests on the understanding of attributive adjectives as
substantive-dependent adjectives, rather than as adjectives, complex predicates with
which are inferentially irregular.
What Is an Attributive Adjective?
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4. So What Is an Attributive Adjective?
At this point we appear to have on our hands two different accounts of what an attributive
adjective is. According to the one suggested by Geach’s treatment of ‘big’, ‘small’, ‘forged’,
and ‘putative’, an attributive adjective is an adjective that when combined with a noun
forms an inferentially irregular predicate. According to the other account, suggested by
Geach’s treatment of ‘good’ and ‘bad’, an attributive adjective is a substantive-dependent
adjective. We shall argue that, of the two, only the latter identifies a genuine logical
characteristic of adjectives. The inferential irregularity of complex predicates using a
given adjective is better regarded as a manifestation of attributivity than as a defining
mark of it.
If attributivity is to be defined in terms of inferential irregularity, there are two ways
of accomplishing the task. One is to say that an adjective is attributive just in case some
complex predicate with it is inferentially irregular. Such a definition follows Geach’s own
formulation, according to which an adjective is predicative just in case some complex
predicate with it fails to ‘split up logically’. But it is easily seen that on this definition an
adjective can be counted as ‘attributive’ for reasons that have nothing to do with its logical
character; for it is conceivable that, just as there are substantive-dependent adjectives,
there could be adjective-dependent nouns. Imagine, for example, a noun ‘nort’ that works
by negating the adjective with which it is combined; or a noun ‘bleve’ that indicates that
the adjective with which it is combined is believed to hold of that of which the adjective–
noun combination is predicated. Thus, to say, e.g., ‘That book is a red nort’ would be as
much as to say ‘That book is not red’, and to say ‘Jones is a dead bleve’ would be
equivalent to saying, ‘Jones is believed dead’. Clearly, predicates formed of such nouns
would be inferentially irregular: from ‘That book is a red nort’ one could not infer ‘That
book is red’, nor from ‘Jones is a dead bleve’ could one infer ‘Jones is dead’. If the English
language contained such nouns, it would be possible to form an inferentially irregular
predicate from any adjective that could be intelligibly combined with them. In such a
scenario, the class of adjectives that can be made to count as ‘attributive’ by the given
definition threatens to extend over all adjectives in the language. It may well be that no
What Is an Attributive Adjective?
11
adjective-dependent nouns exist in English, or in any other natural language. But the
conceivability of such nouns shows that the proposed definition is capable of classifying
adjectives as ‘attributive’ regardless of their logical character.
The other option is to say that an adjective is attributive just in case every complex
predicate with it is inferentially irregular. Such a definition will not have the problem just
mentioned, for if an adjective forms an inferentially irregular complex predicate with any
noun with which it can be intelligibly combined, whether the noun is adjective-dependent
or not, then it must have a distinctive logical character by which it does so. The definition,
however, does not tell us what this logical character is. It specifies which adjectives are
attributive, but gives no account of what makes them so.
We can solve both problems by identifying attributivity with substantive-dependence.
An attributive adjective may be defined as an adjective that cannot be used to make a
logically complete predication unless it modifies some substantive; or, in slightly different
phrasing, as an adjective that forms predicable terms through, and only through,
combination with substantives.14
It may clarify the meaning of this definition to return to the contrast with predicative
adjectives. A predicative adjective may be applied either by itself or in combination with a
noun. In the latter case, adjective and noun form a compound term, the truth-value of an
application of which is determined by those of the applications of the component terms.
E.g., ‘That is a red car’ is true just in case ‘That is red’ and ‘That is a car’ are both true of
the object in question. An attributive adjective, by contrast, can be applied only in
combination with a noun. A term thus formed—‘good car’, ‘putative father’, ‘big flea’,
14. Scott Soames may be thought to suggest a similar conception when he describes
certain adjectives—‘big’ and ‘good’ among them—as ‘predicate modifiers’ (Philosophical
Analysis in the Twentieth Century, volume 2 (Princeton: Princeton University Press,
2003), 149–150). He even cites Geach’s essay with approval in this connection. However,
he offers no explanation of what a predicate modifier is; nor is it clear how to apply what
he says about the workings of ‘big’ and ‘good’ to other attributive adjectives such as
‘putative’, ‘forged’, ‘real’, etc. An account much closer to our own, though advanced without
reference to Geach, may be found in W. V. Quine’s brief remarks on what he terms
‘syncategorematic’ adjectives, in Word and Object (Cambridge, Mass.: M. I. T. Press,1960),
103.
What Is an Attributive Adjective?
12
etc.—is complex, but not compound:15 its sense is a function of the senses of each of the
component expressions, but the truth-value of an application of the complex term cannot
be determined by applying the two component expressions separately; for one of them,
namely the adjective, has no truth- or falsehood-yielding application by itself.
This definition also makes possible a straightforward account of the connection
between attributivity and inferential irregularity; for it is easily shown that any complex
predicate with a substantive-dependent adjective is necessarily inferentially irregular.
Suppose, for instance, that ‘A’ is a substantive-dependent adjective, ‘B’ a noun with which
it may be combined, and ‘s’ a possible subject of predication. Since ‘A’ is substantivedependent, ‘s is A’ has no truth-value: it therefore cannot be inferred from ‘s is an A B’.
Thus, applications of ‘is an A B’ deviate in at least one respect from the forms that govern
logical conjunctions. In general terms, any complex predicate using an attributive
adjective must be inferentially irregular in at least the specified respect. It follows that
the proposed definition is compatible with the use of sample arguments to prove the
attributivity of adjectives, provided that none of the nouns used in the arguments are
adjective-dependent ones. (The specified condition will be otiose if there are no such nouns
in the language.)
To be sure, the impossibility of inference from ‘s is an A B’ to ‘s is A’ is not the only
variety of inferential irregularity that complex predicates using attributive adjectives can
exhibit: it is merely the one variety that necessarily attends every such adjective. Other
varieties are easily found. E.g., from ‘Smith is an alleged thief’ one cannot infer ‘Smith is a
thief’, and from ‘Daisy is a small elephant’ and ‘Every elephant is an animal’ one cannot
infer ‘Daisy is a small animal’, although one can infer ‘Daisy is an elephant’. On the other
hand, complex predicates using certain attributive adjectives do not exhibit any form of
inferential irregularity beyond the kind that marks all complex predicates using
attributive adjectives. E.g., from ‘This is a real banknote’ one can draw exactly those
conclusions which one can draw from ‘This is a banknote’. The variety of ways in which
attributive adjectives manifest inferential irregularity owes to the variety of ways in
15. Contra Soames, who describes the schematic term ‘good N’ as a ‘compound
predicate’ (151).
What Is an Attributive Adjective?
13
which such adjectives logically depend on the nouns with which they combine. There is no
way to investigate these varieties without examining in detail the adjectives concerned.
But there is no way to begin that task without first getting clear on what it means for an
adjective to be attributive. We leave the former task for another occasion, but we believe
that we have accomplished the latter.